## Related questions with answers

Methane $\left(\mathrm{CH}_4\right)$ at $25^{\circ} \mathrm{C}, 1 \mathrm{~atm}$ enters a furnace operating at steady state and burns completely with $140 \%$ of theoretical air entering at $400 \mathrm{~K}, 1\ \text{atm}$. The products of combustion exit at $700 \mathrm{~K}, 1 \mathrm{~atm}$. Kinetic and potential energy effects are negligible. If the rate of heat transfet from the furnace to the surroundings is $400 \mathrm{~kW}$, determine the mass flow rate of methane, in $\mathrm{kg} / \mathrm{s}$.

Solution

VerifiedWrite the balanced chemical equation of $CH_4$ for complete combustion with theoretical amount of dry air

$CH_4+ \alpha (O_2+3.76N_2)\rightarrow \beta CO_2+\gamma H_2O+\omega N_2$

( $\therefore$ 3.76 moles of $N_2$ accompany each mole of $O_2$ in the air)

By applying conservation of mass principle to carbon hydrogen Oxygen and nitrogen respectively.

C : $\rightarrow \beta= 1$

H : $\rightarrow 2 \gamma=4$

O : $\rightarrow 2 \alpha=2 \beta+\gamma$

$N_2$ : $\rightarrow \alpha(3.76)=\omega$

By solving,

$\alpha = 2$

$\beta=1$

$\gamma=2$

$\omega=7.52$

Therefore the balanced chemical equation is,

$CH_4+ 2 (O_2+3.76N_2) \rightarrow CO_2+2 H_2O+7.52 N_2$

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